slaexc (l) - Linux Manuals

slaexc: swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

NAME

SLAEXC - swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

SYNOPSIS

SUBROUTINE SLAEXC(
WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO )

    
LOGICAL WANTQ

    
INTEGER INFO, J1, LDQ, LDT, N, N1, N2

    
REAL Q( LDQ, * ), T( LDT, * ), WORK( * )

PURPOSE

SLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation. T must be in Schur canonical form, that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elemnts equal and its off-diagonal elements of opposite sign.

ARGUMENTS

WANTQ (input) LOGICAL
= .TRUE. : accumulate the transformation in the matrix Q;
= .FALSE.: do not accumulate the transformation.
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) REAL array, dimension (LDT,N)
On entry, the upper quasi-triangular matrix T, in Schur canonical form. On exit, the updated matrix T, again in Schur canonical form.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) REAL array, dimension (LDQ,N)
On entry, if WANTQ is .TRUE., the orthogonal matrix Q. On exit, if WANTQ is .TRUE., the updated matrix Q. If WANTQ is .FALSE., Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.
J1 (input) INTEGER
The index of the first row of the first block T11.
N1 (input) INTEGER
The order of the first block T11. N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block T22. N2 = 0, 1 or 2.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
= 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged.

Pages related to slaexc

  • slaexc (3)
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  • slaebz (l) - contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
  • slaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
  • slaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • slaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
  • slaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
  • slaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
  • slaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
  • slaed6 (l) - computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true